Taxonomies are fundamental to many real-world applications in various domains, serving as structural representations of knowledge. To deal with the increasing volume of new concepts needed to be organized as taxonomies, researchers turn to automatically completion of an existing taxonomy with new concepts. In this paper, we propose TaxoEnrich, a new taxonomy completion framework, which effectively leverages both semantic features and structural information in the existing taxonomy and offers a better representation of candidate position to boost the performance of taxonomy completion. Specifically, TaxoEnrich consists of four components: (1) taxonomy-contextualized embedding which incorporates both semantic meanings of concept and taxonomic relations based on powerful pretrained language models; (2) a taxonomy-aware sequential encoder which learns candidate position representations by encoding the structural information of taxonomy; (3) a query-aware sibling encoder which adaptively aggregates candidate siblings to augment candidate position representations based on their importance to the query-position matching; (4) a query-position matching model which extends existing work with our new candidate position representations. Extensive experiments on four large real-world datasets from different domains show that \TaxoEnrich achieves the best performance among all evaluation metrics and outperforms previous state-of-the-art methods by a large margin.